# How do you solve 10=-2/3(4x+5)?

Feb 20, 2016

$x = - 5$

Working out shown in a lot of detail!

#### Explanation:

Given:$\text{ } 10 = \textcolor{b r o w n}{\textcolor{b l u e}{- \frac{2}{3}} \left(4 x + 5\right)}$

Multiply out the brackets giving:

" "10= color(brown)({color(blue)((-2/3))xx4x }" "+" "{color(blue)((-2/3))xx5})

The 'squiggly' brackets (braces) are only there to group parts to make understanding easier. They serve no other purpose

$10 = - \frac{8}{3} x - \frac{10}{3}$

Add $\textcolor{b l u e}{\frac{10}{3}}$ to both sides

$\textcolor{b r o w n}{10 \textcolor{b l u e}{+ \frac{10}{3}} = - \frac{8}{3} x - \frac{10}{3} \textcolor{b l u e}{+ \frac{10}{3}}}$

$\frac{40}{3} = - \frac{8}{3} x + 0$

$\frac{40}{3} = - \frac{8}{3} x$

Multiply both sides by$\textcolor{b l u e}{3}$

$\frac{40}{\cancel{3}} \times \cancel{\textcolor{b l u e}{3}} = - \frac{8}{\cancel{3}} x \times \cancel{\textcolor{b l u e}{3}}$

Divide both sides by 8, divide by 8 is the same as $\times \frac{1}{8}$

$\frac{40}{8} = - \frac{8}{8} x$

So $\text{ "-x=5" }$ Notice the $x$ is negative

Multiply both sides by (-1) giving

$x = - 5$